Kant on fundamental geometrical relations

Equality, similarity and congruence are essential elements of Kant’s theory of geometrical cognition; nevertheless, Kant’s account of them is not well understood. This paper provides historical context for treatments of these geometrical relations, presents Kant’s views on their mathematical definitions, and explains Kant’s theory of their cognition. It also places Kant’s theory within the larger context of his understanding of the quality-quantity distinction. Most importantly, it argues that the relation of equality, in conjunction with the categories of quantity, plays a pivotal and wide-ranging role in Kant’s account of mathematical cognition.
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DOI 10.1515/agph.2005.87.2.117
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Jeremy Heis (2014). Kant on Real Definitions in Geometry. Canadian Journal of Philosophy 44 (5-6):605-630.

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